/*
 * jidctflt.c
 *
 * Copyright (C) 1994, Thomas G. Lane.
 * This file is part of the Independent JPEG Group's software.
 * For conditions of distribution and use, see the accompanying README file.
 *
 * This file contains a floating-point implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * This implementation should be more accurate than either of the integer
 * IDCT implementations.  However, it may not give the same results on all
 * machines because of differences in roundoff behavior.  Speed will depend
 * on the hardware's floating point capacity.
 *
 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
 * on each row (or vice versa, but it's more convenient to emit a row at
 * a time).  Direct algorithms are also available, but they are much more
 * complex and seem not to be any faster when reduced to code.
 *
 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
 * JPEG textbook (see REFERENCES section in file README).  The following code
 * is based directly on figure 4-8 in P&M.
 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
 * possible to arrange the computation so that many of the multiplies are
 * simple scalings of the final outputs.  These multiplies can then be
 * folded into the multiplications or divisions by the JPEG quantization
 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
 * to be done in the DCT itself.
 * The primary disadvantage of this method is that with a fixed-point
 * implementation, accuracy is lost due to imprecise representation of the
 * scaled quantization values.  However, that problem does not arise if
 * we use floating point arithmetic.
 */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"        /* Private declarations for DCT subsystem */

#ifdef DCT_FLOAT_SUPPORTED


/*
 * This module is specialized to the case DCTSIZE = 8.
 */

#if DCTSIZE != 8
Sorry, this code only copes with 8 x8 DCTs.  /* deliberate syntax err */
    #endif


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce a float result.
 */

#define DEQUANTIZE( coef, quantval )  ( ( (FAST_FLOAT) ( coef ) ) * ( quantval ) )


/*
 * Perform dequantization and inverse DCT on one block of coefficients.
 */

GLOBAL void
jpeg_idct_float( j_decompress_ptr cinfo, jpeg_component_info * compptr,
                 JCOEFPTR coef_block,
                 JSAMPARRAY output_buf, JDIMENSION output_col ) {
    FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
    FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
    FAST_FLOAT z5, z10, z11, z12, z13;
    JCOEFPTR inptr;
    FLOAT_MULT_TYPE * quantptr;
    FAST_FLOAT * wsptr;
    JSAMPROW outptr;
    JSAMPLE * range_limit = IDCT_range_limit( cinfo );
    int ctr;
    FAST_FLOAT workspace[DCTSIZE2];/* buffers data between passes */
    SHIFT_TEMPS

    /* Pass 1: process columns from input, store into work array. */

    inptr = coef_block;
    quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
    wsptr = workspace;
    for ( ctr = DCTSIZE; ctr > 0; ctr-- ) {
        /* Due to quantization, we will usually find that many of the input
         * coefficients are zero, especially the AC terms.  We can exploit this
         * by short-circuiting the IDCT calculation for any column in which all
         * the AC terms are zero.  In that case each output is equal to the
         * DC coefficient (with scale factor as needed).
         * With typical images and quantization tables, half or more of the
         * column DCT calculations can be simplified this way.
         */

        if ( ( inptr[DCTSIZE * 1] | inptr[DCTSIZE * 2] | inptr[DCTSIZE * 3] |
               inptr[DCTSIZE * 4] | inptr[DCTSIZE * 5] | inptr[DCTSIZE * 6] |
               inptr[DCTSIZE * 7] ) == 0 ) {
            /* AC terms all zero */
            FAST_FLOAT dcval = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] );

            wsptr[DCTSIZE * 0] = dcval;
            wsptr[DCTSIZE * 1] = dcval;
            wsptr[DCTSIZE * 2] = dcval;
            wsptr[DCTSIZE * 3] = dcval;
            wsptr[DCTSIZE * 4] = dcval;
            wsptr[DCTSIZE * 5] = dcval;
            wsptr[DCTSIZE * 6] = dcval;
            wsptr[DCTSIZE * 7] = dcval;

            inptr++;    /* advance pointers to next column */
            quantptr++;
            wsptr++;
            continue;
        }

        /* Even part */

        tmp0 = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] );
        tmp1 = DEQUANTIZE( inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] );
        tmp2 = DEQUANTIZE( inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] );
        tmp3 = DEQUANTIZE( inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] );

        tmp10 = tmp0 + tmp2;/* phase 3 */
        tmp11 = tmp0 - tmp2;

        tmp13 = tmp1 + tmp3;/* phases 5-3 */
        tmp12 = ( tmp1 - tmp3 ) * ( (FAST_FLOAT) 1.414213562 ) - tmp13;/* 2*c4 */

        tmp0 = tmp10 + tmp13;/* phase 2 */
        tmp3 = tmp10 - tmp13;
        tmp1 = tmp11 + tmp12;
        tmp2 = tmp11 - tmp12;

        /* Odd part */

        tmp4 = DEQUANTIZE( inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] );
        tmp5 = DEQUANTIZE( inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] );
        tmp6 = DEQUANTIZE( inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] );
        tmp7 = DEQUANTIZE( inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] );

        z13 = tmp6 + tmp5;  /* phase 6 */
        z10 = tmp6 - tmp5;
        z11 = tmp4 + tmp7;
        z12 = tmp4 - tmp7;

        tmp7 = z11 + z13;   /* phase 5 */
        tmp11 = ( z11 - z13 ) * ( (FAST_FLOAT) 1.414213562 );/* 2*c4 */

        z5 = ( z10 + z12 ) * ( (FAST_FLOAT) 1.847759065 );/* 2*c2 */
        tmp10 = ( (FAST_FLOAT) 1.082392200 ) * z12 - z5;/* 2*(c2-c6) */
        tmp12 = ( (FAST_FLOAT) -2.613125930 ) * z10 + z5;/* -2*(c2+c6) */

        tmp6 = tmp12 - tmp7;/* phase 2 */
        tmp5 = tmp11 - tmp6;
        tmp4 = tmp10 + tmp5;

        wsptr[DCTSIZE * 0] = tmp0 + tmp7;
        wsptr[DCTSIZE * 7] = tmp0 - tmp7;
        wsptr[DCTSIZE * 1] = tmp1 + tmp6;
        wsptr[DCTSIZE * 6] = tmp1 - tmp6;
        wsptr[DCTSIZE * 2] = tmp2 + tmp5;
        wsptr[DCTSIZE * 5] = tmp2 - tmp5;
        wsptr[DCTSIZE * 4] = tmp3 + tmp4;
        wsptr[DCTSIZE * 3] = tmp3 - tmp4;

        inptr++;        /* advance pointers to next column */
        quantptr++;
        wsptr++;
    }

    /* Pass 2: process rows from work array, store into output array. */
    /* Note that we must descale the results by a factor of 8 == 2**3. */

    wsptr = workspace;
    for ( ctr = 0; ctr < DCTSIZE; ctr++ ) {
        outptr = output_buf[ctr] + output_col;
        /* Rows of zeroes can be exploited in the same way as we did with columns.
         * However, the column calculation has created many nonzero AC terms, so
         * the simplification applies less often (typically 5% to 10% of the time).
         * And testing floats for zero is relatively expensive, so we don't bother.
         */

        /* Even part */

        tmp10 = wsptr[0] + wsptr[4];
        tmp11 = wsptr[0] - wsptr[4];

        tmp13 = wsptr[2] + wsptr[6];
        tmp12 = ( wsptr[2] - wsptr[6] ) * ( (FAST_FLOAT) 1.414213562 ) - tmp13;

        tmp0 = tmp10 + tmp13;
        tmp3 = tmp10 - tmp13;
        tmp1 = tmp11 + tmp12;
        tmp2 = tmp11 - tmp12;

        /* Odd part */

        z13 = wsptr[5] + wsptr[3];
        z10 = wsptr[5] - wsptr[3];
        z11 = wsptr[1] + wsptr[7];
        z12 = wsptr[1] - wsptr[7];

        tmp7 = z11 + z13;
        tmp11 = ( z11 - z13 ) * ( (FAST_FLOAT) 1.414213562 );

        z5 = ( z10 + z12 ) * ( (FAST_FLOAT) 1.847759065 );/* 2*c2 */
        tmp10 = ( (FAST_FLOAT) 1.082392200 ) * z12 - z5;/* 2*(c2-c6) */
        tmp12 = ( (FAST_FLOAT) -2.613125930 ) * z10 + z5;/* -2*(c2+c6) */

        tmp6 = tmp12 - tmp7;
        tmp5 = tmp11 - tmp6;
        tmp4 = tmp10 + tmp5;

        /* Final output stage: scale down by a factor of 8 and range-limit */

        outptr[0] = range_limit[(int) DESCALE( (INT32) ( tmp0 + tmp7 ), 3 )
                                & RANGE_MASK];
        outptr[7] = range_limit[(int) DESCALE( (INT32) ( tmp0 - tmp7 ), 3 )
                                & RANGE_MASK];
        outptr[1] = range_limit[(int) DESCALE( (INT32) ( tmp1 + tmp6 ), 3 )
                                & RANGE_MASK];
        outptr[6] = range_limit[(int) DESCALE( (INT32) ( tmp1 - tmp6 ), 3 )
                                & RANGE_MASK];
        outptr[2] = range_limit[(int) DESCALE( (INT32) ( tmp2 + tmp5 ), 3 )
                                & RANGE_MASK];
        outptr[5] = range_limit[(int) DESCALE( (INT32) ( tmp2 - tmp5 ), 3 )
                                & RANGE_MASK];
        outptr[4] = range_limit[(int) DESCALE( (INT32) ( tmp3 + tmp4 ), 3 )
                                & RANGE_MASK];
        outptr[3] = range_limit[(int) DESCALE( (INT32) ( tmp3 - tmp4 ), 3 )
                                & RANGE_MASK];

        wsptr += DCTSIZE;   /* advance pointer to next row */
    }
}

#endif /* DCT_FLOAT_SUPPORTED */
